A new method for essential boundary conditions imposition in explicit meshless methods

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    Abstract

    In this paper we present a new technique of enforcing Essential Boundary Conditions (EBC) in Meshless Methods (MMs) based on the Element Free Galerkin (EFG) principles. Imposing EBC is a fundamental issue in MMs. The imposition of prescribed displacement values on the boundary in MMs based on approximating shape functions is not as straightforward as in the Finite Element Method (FEM) because the meshless shape functions are generally not interpolating at nodes. Furthermore, many techniques of enforcing EBC are not compatible with explicit time integration schemes. This paper describes a new method of imposing EBC in EFG based MMs suitable for explicit time integration, named Essential Boundary Conditions Imposition in Explicit Meshless (EBCIEM). The effectiveness of the proposed method is demonstrated using both 2D and 3D numerical examples.

    Original languageEnglish
    Pages (from-to)94-104
    Number of pages11
    JournalEngineering Analysis with Boundary Elements
    Volume80
    DOIs
    Publication statusPublished - 1 Jul 2017

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    Meshless Method
    Explicit Methods
    Boundary conditions
    Element-free Galerkin
    Explicit Time Integration
    Meshless
    Shape Function
    Finite Element Method
    Finite element method
    Numerical Examples
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    Cite this

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    title = "A new method for essential boundary conditions imposition in explicit meshless methods",
    abstract = "In this paper we present a new technique of enforcing Essential Boundary Conditions (EBC) in Meshless Methods (MMs) based on the Element Free Galerkin (EFG) principles. Imposing EBC is a fundamental issue in MMs. The imposition of prescribed displacement values on the boundary in MMs based on approximating shape functions is not as straightforward as in the Finite Element Method (FEM) because the meshless shape functions are generally not interpolating at nodes. Furthermore, many techniques of enforcing EBC are not compatible with explicit time integration schemes. This paper describes a new method of imposing EBC in EFG based MMs suitable for explicit time integration, named Essential Boundary Conditions Imposition in Explicit Meshless (EBCIEM). The effectiveness of the proposed method is demonstrated using both 2D and 3D numerical examples.",
    keywords = "Element free galerkin, Essential boundary conditions, Explicit time integration, Meshless methods, Non-interpolating shape functions",
    author = "Joldes, {Grand Roman} and Habib Chowdhury and Adam Wittek and Karol Miller",
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    AU - Joldes, Grand Roman

    AU - Chowdhury, Habib

    AU - Wittek, Adam

    AU - Miller, Karol

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    N2 - In this paper we present a new technique of enforcing Essential Boundary Conditions (EBC) in Meshless Methods (MMs) based on the Element Free Galerkin (EFG) principles. Imposing EBC is a fundamental issue in MMs. The imposition of prescribed displacement values on the boundary in MMs based on approximating shape functions is not as straightforward as in the Finite Element Method (FEM) because the meshless shape functions are generally not interpolating at nodes. Furthermore, many techniques of enforcing EBC are not compatible with explicit time integration schemes. This paper describes a new method of imposing EBC in EFG based MMs suitable for explicit time integration, named Essential Boundary Conditions Imposition in Explicit Meshless (EBCIEM). The effectiveness of the proposed method is demonstrated using both 2D and 3D numerical examples.

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    KW - Essential boundary conditions

    KW - Explicit time integration

    KW - Meshless methods

    KW - Non-interpolating shape functions

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